Solution
Professor Landsberg (who taught Physics 102 in Spr. '98) is nearsighted. Without glasses he cannot see clearly any objects that are more than 0.5 m away. His power of accommodation is 4 diopters.
(a) Are Prof. Landsberg's glasses thicker in the middle or at the edges?

Answer: Since Prof. Landsberg is nearsighted he has too much focusing power. He therefore needs to wear diverging lenses, which are thicker at the edges.

(b) What power corrective lens does he wear?

Answer: Prof. Landsberg needs to obtain glasses that will move his far point to an infinite distance. Without glasses his focusing power, when his eyes are set to minimum power, is
P = 1/f = 1/s + 1/s' = 2 D + 50 D = 52 D
since the image is on the retina 2 cm behind the lens of the eye and the object distance is 0.5 m. For Prof. Landsberg to see clearly objects that are far away, we must increase s, such that 1/s goes to 0. Thus Prof. Landsberg's focusing power needs to be reduced by 2 D. He therefore wears corrective lenses with a power of - 2 D.

(c) Without glasses, what is the closest distance he can hold a book to his face and still read it clearly?

Answer: Without glasses Prof. Landsberg has a focusing power of 52 D at his far point. Since his power of accommodation is 4 D, his focusing power at his near point will be 56 D.
P = 56 D = 1/s + 1/s' = 1/s + 50 D => 1/s = 6 D so that s=17 cm.
So Prof. Landsberg's near point is at 17 cm without his glasses.


Physics 102 HW page